Feedback amplifier filter



Jam., 2, w40, H. A. WHEELER FEEDBACK AMPLIFIER FILTER Filed May 9, 19382 Sheets-Sheet l INVENTOR you) AWHEELR BY ATTORNEY j. 2, w49. H. A.WHEELER FEEDBACK AMPLIFIER 'FILTER Filed May 9, 1958 2 Sheets-Sheet 2ATTORNEY Harold A. eeler, Grt Neck, lil.

l., imgnor to `easeltine ilorration, e corporation oi DelawareApplication y t, luid, Serial No. 296,71@

, invention relates to signal-inlog vacuum-tube stares and particularlyto such stares oi a. type comprisine a feedback circuit in which theulter properties of the stage are `e utilised to incorporate the stageas one oi a series oi conduent iilter networks. Specically the inventioncomprises a network in which the inocuo pedance characteristics of thefeedback stare are matched in the confluent series oi netiii vvorirswith the image impedance characteristics oi other 1|; z lar etapes orwith the image impedance characteristics ci conventional nlter sections.

vacuo-tube stares comprising feed-bach cirii! cuits have been utilisedtor various purposes.

r example, in modulated-carrier signal-translutinp systems, stagescomprisinp a pair oi terminal circuits and a vacuum-tube coupling meanscouplinp the terminal circuits in one direction, 2d toeether with anadditional coupling means coupiinn the circuits in the oppositedirectiomhave been utilized as hand-pass selectors in the intermediate-frequency channel or superheierof.`

sil receivers. in prior art circuit arrangetii ments utilizing anampliher stare with feedback,

the terminal circuits oi the stage have been indvidually loaded ordamped by terminal resistai'ices to provide suitable damping for thestage. hs thus terminated, the ieedbacir stages of the prior it art havehad the required damping within the ieedbact stades themselves and havebeen loosely coupled to adjacent similar stages or to other circuits. lisuch arrangements are utilized lor passinc a wide band oi irequencies,the width oi the su pass band is limited by the inherent capacitances ofthe tubes and the circuit elements. Also, the wr or an amplifiercomprising such a stage is muterially decreased by the elements providedfor individually damping the terminal circuits of the im stese.

it is an object of the invention to provide a ieedbacu vacuum-tubeampliiier and iilter having a relatively large amplification and passinga wide hand oi ireuuencies.

lt is another object of the invention to provide u, conduent filternetwork comprising a nlter secu tion including a vacuum-tube coupling inone direction and an additional coupling in the other cation, the stagebeing matched with adjacent 5@ sections oi the network on an imageimpedance lt is a iurthcrobiect oi. the invention to provide a confluentfilter network comprising an active iiitcr section. as contrasted witha-passive ter section, at least one terminal circuit of' (ci. ira-in) lwhich is matched with an adjacent section of the network on an imaseimpedance basis.

In accordance with the invention, there is provided a filter sectioncomprising a. vacuum-tube coupling in one direction and an additionalcou- ..5 pling in the other direction, at least one terminal circuit ofthe stage being matched on an image impedance basis with an adjacentterminal circuit oi en adjacent lter section to which the stare iscoupled in a confluent network.

In one embodiment of the invention, a hlter section comprises avacuum-tube amplifier stage including terminal circuits, a vacuum-tubecouplinu means coupling the terminal circuits in the iorward direction,and a' second vacuum-tube it coupling means coupling the terminalcircuits in the backward direction. The input and output terminals ofthe stage are individually coupled to circuits having constant-lt imageimpedances. The terminal circuits of the lter section and the E relativetransconductances of the vacuum tubes utilized in the stage are soproportioned that the image impedance at each pair of terminals closelymatches the constant-Ic image impedance of the adjacent meer section towhich a is directly couit pled. This manner oi coupling the amplierstage to adjacent nlter sections obviates the necessityoi individuallyloading or damping each oi the terminal circuits of the stage, since theloadine or damping of the entire networlr is adequately secured at theinput and output terminals oi the system asa whole. The filterproperties of the feedback stage of the invention make it possible toinsert-additional filter sections between the stages for any purpose forwhich they are useful. Added sections may be inserted for securing moreattenuation outside the pass band, for securing phase correction withinthe band, or for both purposes.

In a preferred embodiment of the invention, t0

the vacuum-tube stage comprises terminal circuits coupled in the forwarddirection by s. vacuumftube transconductance coupling means4 and.coupled in the backward direction by passive conductance or resistanceVcoupling means. et i phase-shifting circuit may beassociated with. thebackward coupling. means, the amount oi phase shirt being proportionedto e'ect regeneration just suillcient to compensate, at the cutofffrequency, for the losses caused by the sell-conductance or otherdissipation in the terminal circuits and coupling means of the stese.The result is to maintain the sharpness of cutoi! which would beobtained in a nlter if the nlter had no inherent dissipation.

For a better lmderstandingof the invention, together with other andfurther objects thereof, reference is had to the following description,taken in connection with the accompanying drawings, and its scope willbe pointed out iri the appended claims.

Fig. 1 of the drawings is a simplified circuit diagram of a low-passampliiler illter of the invention, an image impedance of the vacuum-tubefeedback section of which is matched with that of an adjacent circuit toform a confluent series of sections; Figs. 2te-2e, inclusive, are graphsillustrating certain theoretical characteristics of the feed-back stageof Fig. 1; Fig. 3 is a simplified circuit diagram of a feedback ltersimilar to that of Fig. 1 except that a conductance feedback circuit isprovided in the feedback section of the network; Fig. 4 is a circuitdiagram of a band-pass amplifier ilter corresponding in type to thelow-pass lter of Fig. 1; Figs. 5 and 6 are circuit diagrams of differenttypes of conuent amplier filters of the invention, each comprisingl twofeedback sections.

Referring now more particularly to Fig. 1. there is shown a vacuum-tubeamplifier stage comprising one of a conuent series of iilter sections.The stage comprises input terminals 8, 8 and output terminals 1, 1across which are coupled, respectively, condensers C1 and C2,

forming shunt arms of the stage. The terminal circuits are coupled inthe forward direction by a unidirectional coupling means primarilyvtransconductive, such as a vacuum tube I and are coupled with oppositepolarity in the backward direction by a vacuum tube II. Sources ofoperating potentials (not shown) and other electrodes such as screengrids, if desired, are provided for tubes I0 and II in a conventionalmanner. The image impedance of the circuit between the input terminalst, 6 is indicated by Z'. Vacuum tube I I is so connected as to haveeifectively a positive transconductance in contrast to the ordinarynegative transconductance of a vacuum tube; that is, the output circuitof vacuum tube II is taken from ascreen circuit. This manner ofutilizing a vacuum tube to procure positive transconductance is morefully explained in United States Letters Patent 1,997,865, granted.April` 16, 1985, on the application of Harold A. Wheeler. The outputterminals 1, 1 of the amplifier stage are connected to `a constant-kfilter section comprising series inductance arm I2 and shunt condenserarms i3 and I4. Condensers Il and Il have approximately the same valueof capacitance es condenser Cn. 'I'he output terminals U, 8 of theseries of networks shown may be coupled, with image impedance matching,to any other network. The image impedance at the output terminals I, 8is indicated by Z", the image impedance termination of theoutput circuitbeing represented by resistor R". l

'I'he operation of the filter network described may be explained withreference to Figs. 2a'2e, inclusive, which represent certain theoreticalcharacteristics of thel feedback ampliiier iilter section of Fig. 1,'each of the ilgures having frequency as the abscissae. Thus, Fig. 2arepresents the impedance of the feedback amplifier filter section ofFig. 1 on 'either side, with the other side on short'circuit: Fig. 2bshows the' the feedback amplier illter section. The upper and lower4dotted-line curves of Fig. 2e show the actual phase shift for a stagehaving, respectively, negative and positive forward transconductance. Itwill be understood that the characteristic curves of Figs. 2a-2c,inclusive, are equally applicable at either the input terminals 6, 6 orthe output terminals 1, 1.

Thus it is seen that the feedback amplifier filter section has input andoutput image impedances which exactly conform to constant-Ic mid-shuntimage impedances. The system may, therefore, be connected in a conuentseries of networks on an image impedance basis with other similaramplifier stages or with filter sections having the constant-Ic form ofimage impedance. The low-pass amplifier filter stage shown has a cutofffrequency:

L :one-half the inductance of winding I2; g12=the transconductance ofvacuum tube I0; gz1=the transconductance of vacuum'tube II.

Resistor R', representing the image impedance of both circuits connectedat the terminals 8, 6, and resistor R", representing the image impedanceof both circuits connected at the terminals 8, 8, or terminatingresistors to match such image impedances, have the values:

The respective image impedances for any frequency w are:

R z Ufa/F U l R' l 5 The image impedance ratio of the network shown'is:

Ordinarily this image impedance ratio is unity in a low-pass iilternetwork. However, due to the fact that the amplifier filter section ofthe invention is an active section, the image impedance ratio of thecircuit of Fig. 1 can have any desired value. -The gain of the amplifierfilter section of Fig. 1, which is the voltage ratio when connectedbetween equal impedances, is:

2-a El dal K Ordinarily the phase shift of a filter section varies overa range of 180 degrees over the pass band. It will be seen from thephase-frequency curves of Fig. 2e that the phase of the low-pass lanoutput circuit, as in the case of tube II in Fig. l, is one way ofsecuring a negative transconductance. Other means for accomplishing thisare two conventional tubes coupled in cascade in the normal manner, ora. phase-reversing transformer utilized with a. normal tube having anegative transconductance. Preferably the tubes utilized in the iilternetworks oi the invention have a very small anode conductanceI which isa property of high-mu tubes, such as screen-grid tubes or high-mutriodes. if the ampliiier filter section is designed for operation atvery high frequencies, the tubes must be shielded against internalcapacitive coupling and in such cases the use of screen-grid tubes isessential.

The circuit oi Fig. 3 is, in general, similar to the circuit oi Fig. land similar circuit elements have been given identical referencenumerals. In the circuit oi Fig. 3 the coupling provided by vacuum tubeii ci Fig. l, oi opposite polarity to the couv pling oi vacuum tube it,has been replaced by a dit primarily conductive coupling. Thisconductive coupling is obtained by means of a resistor it connecteddirectly between the anode and the grid oi vacuum tube it. Ii theconductance Gs oi" the feedback circuit comprising resistor it is muchless than the transconductance gm ci' vacnum tube it, the operation oithe circuit ci Fig. Ii is in all respects similar to that of the circuitoi' Fig. i. vl'he ampliier nlter section of Fig. 3 has thecharacteristic oi a mid-shunt constant-7c image impedance across each ofcondensers C1 and f G2 similar to that across corresponding elements inthe circuit oi? iilig. l. The following additional equations erpress theedective transconductances in the circuit oi' ilig. 3:

l dir-tdw. Gs (7) di: Ga (s) lin Fig. 'i there is shown a bandiiiterarnplifier section ci the invention connected in a titl continentnetwork with age impedance matching. The circuit is generally similar tothe circuit ci the low-pass iilter oi tig. l and similar circuitelements have been given identical reierence numerals. in addition tothe circuit elements ci iiig. l, ilig. a comprises an inductance linconnected in parallel with condenser C1, and an inductance in connectedin parallel with condenser Cz. The' positive transconductance in theicedbacir circuit oi Fig. d is obtained by vacuum tube Il i connected inthe normal manner together with proper polarity ci the mutualinductances ci the tranciormers provided by s it and iii coupled toinductances in and Le, respectively. The inductance element it oi theconstant-ic section oi' the circuit oi Fig. i has been replaced in Fig.i by inductance network it, the reactive constants oi which edectivel-yprovide inductance elements for a bund-pass moi-lined constant-it nitersection comprising shunt condenser-s it and iii. The operation oi thecircuit of Fig. d may be understood trom the description ci theoperation oi" the circuit or Fig. i given above. The following equationsdenne the characteristics ci the amplifier filter. section oi Fig. t:

White-JEJ- i/CxLi 1f CzLi i i ww1 m C-lj 5W,

where w24-:mean ir wir nor ot the band;

w=lower cutod irequency ci the band; m-upper cui-.od .frequency of theband. 1

- in the forward direction In Fig. there is shown a. conuent series ofiilter sections coupled with image impedance matching and comprising twoamplier ltersections in accordance with the invention. The rst amplierhlter section comprises a shunt reactive arm including aseries-connected inductance 22 and condenser it and a second shuntreactance arm comprising a condenser 2 I. These shunt reactance arms arecoupled in the forward direction by the vacuum tube 2t and are coupledin the backward direction with opposite polarity by a conductancecoupling with the addition of series inductances 25 and it, resistor itbeing replaced by resistors it', I5". A condenser 2l is connected fromthe Junction between inductances 2t and it and the low-potentialterminal of condenser 2t. Grid-leak resistor it is provided for vacuumtube it, while the resistance of its load circuit is represented byresistor 29. Across the input terminals of the circuit o lFig. 5 isconnected a resistor it matching the image imped ance between theterminals and which is nearly constant over the pass band. Coupled tothe output circuit of `Fig. 51s a constant-lc low-pass filter sectioncomprising series inductance arm ti and shunt arms consisting ofcondensers t2 and 33, the value oi each of which is equal to that ofcondenserti. The second amplier filter section of the circuit ci Fig. 5comprises a shunt capacitance armconsisting of a condenser it and ashunt arm including a series-connected inductance 3E and condenser it.The shunt arm comprising condenser tt and the shunt arm comprisingseries-connected inductance it and condenser it are coupled by vacuumtube t? and are coupled in the backward direction ywith oppositepolarity by a resistor tu. A grid leal; it 'is provided for vacuum tubet?, while resistor dit represents the resistance in the output circuitci' vacuum tube iii. Across the output terminals of the conduent networkoi Fig. 5 is connected a resistor iti matching its image impedance.'@per-ating potentials are provided for the vacuum tubes in aconventional manner, while blocking oo ndensers di, it, dit, and it areprovided to corinne direct currents to their proper channels.

In considering the operation of the circuit oi.v v

liig. 5, it will be seen that the conductance eleu ments it. it" provideaieedback coupling from the output circuit of vacuum tube 2li to theinput circuit thereof. lnductances it, it and condenser il areproportioned to shift the phase of the feedback coupling slightly toprovide regen eration in the amplicr filter section just sufiicient tocompensate, at the cutod frequency, for the losses caused by theieedbacir conductance oi resistors it', it" and the dissipation in theterminal circuits of the stage. The result is that the sharpness ofcutod is maintained just as if the lter had no dissipation. Inductanceelement it provided in the shunt reactance `arm of the input circuit ofvacuum tube 2t completes an mderlved termination having an imageimpedance which matches the constantresistance til. im ductance tti isprovided for the same reason in series with condenser lit; that is, tocomplete an 11i-derived termination for the output circuit of theamplifier lter section comprising tube ti which more closely matchesthel impedance ot the sections oi' the invention coupled in cascade in aconfluent band-pass lter network. Thus, the

first amplifier filter section of Fig. 6 comprises a shunt reactance armincluding the secondary winding of transformer 56 and a shunt reactancearm comprising the primary winding 53 of transformer 52. Winding 5| iscoupled in a. forward direction to winding 53 by a vacuum tube 54 and iscoupled in the backward direction with opposite polarity by a c-ircuitcomprising seriesconnected resistor 55 and condenser 56. The electrodecapacitances of tube 54, represented by condensers 5|' and 53', areeffective to tune the transformer windings to which the electrodes-arecoupled. The primary winding'i of transformer 50 is tuned by a shuntcondenser 58 across which is coupled a. resistance element 59representing the impedance of the preceding circuit to which the inputcircuit of Fig. 6 is coupled. The circuit of the second amplifier filtersection of Fig. 6 is in all respects similar to the first amplifierfilter section described above, and comprises a vacuum tube 64 couplingthe secondary winding 6| of transformer 52 in the forward direction tothe primary winding 63 of transformer 62, and a feedback circuitcoupling windings 6I and 63 in the backward direction with oppositepolarity comprising a series-connected resistor 66 and blockingcondenser 61. A shunt condenser 68 is connected across the secondarywinding 69 of transformer 62 to which is coupled resistance 'I0representing the impedance of the succeeding circuit to which the outputterminals of the filter network are coupled. The inherent input andoutput capacitances of vacuum tube Glare represented respectively bycondensers 6I" and 68'. l

The operation of each amplifier filter section of Fig. 6 is similar tothe operation ofthe circuit of Fig. 3, rendering a further descriptionthereof unnecessary. The feedback circuits of Fig. 6 are tapped down ontheir respective transformer windings in order that a lower value ofresistance may be utilized in the feedback circuits and for the purposeof reducing the capacitive coupling associated with the resistanceelements. It will be seen that the circuit of Fig. 6 provides a meansfor coupling two vacuum-tube amplifier filter sections in cascade, therebeing minimum dissipation within the filter stages. The circuit of eachof the amplifier filters` of Fig. 6 is similar to that of Fig. 4 in thateach relates to a band-pass filter. However, the feedback coupling pathsofthe amplifier filters of Fig. 6 are similar to the conductancecoupling including resistor I5 of the low-pass filter of Fig. 3. Thedamping necessary to..provide proper terminal impedances for theamplifier filter sections is secured mainly by resistors 59 and 10 atthe ends of the confluent network.

The coefficient of coupling 1c between windings 53 and 6| of transformer62 is much less than would be required to couple conventional vac-.uum-tube amplifier stages. If Aw is the width of the pass band and wois the mean frequency of the pass band, the required coupling is,

where Asme. This 1s han that required without4 feedback in the adjacentstages.

While there have been described what are at afsasee aimed in theappended claims to cover all: uch changes and modifications as fallwithin the true spirit and scope of the invention.

What is claimed is:

1. A Wave filter network comprising a first filter section having apredetermined image impedance at one end and an active second filtersection comprising input and output pairs of terminals, a reactance armindividual to and. coupled to each of said pairs of terminals,unidirective coupling means betweensaid arms primarilyitransconductivein the direction of coupling, and means coupling said arms with oppositepolarity in the other direction, whereby said second filter section hasa predetermined pass band and a predetermined image impedance across oneof said pairs of terminals, said one of said pairs of terminals beingcoupled to said end of said first filter section, said coupling meansbeing so proportioned with respect to the reactive constants of saidarms that the image impedance of said second filter section matches theimage impedance of said first section at their junction. A

2. A wave filter network comprising a first filter section having apredetermined image impedance at one end and an active second filtersection comprising input and output pairs of terminals, a reactance armindividual to and coupled to each of said pairs of terminals,unidirective coupling means between said arms primarilytransconductivein the direction of coupling, coupling means primarilyconductive coupling said arms with opposite polarity in the otherdirection, whereby said second filter section has a predetermined passband and a predetermined image impedance across one of said pairs ofterminals, said one of said pairs of terminals being coupled to said endof said first filter section, and said coupling means beingl soproportioned with respect to the reactive constants of said arms thatthe image impedance of said second filter section matches the imageimpedance of said first section at vtheir junction.-

3. A wave filter network comprising a first filter section having apredetermined image impedance at one end and a second active filtersection comprising input and output pairs of terminals, a reactance armindividual to and coupled to each of said pairs of terminals,unidirective coupling means between said arms primarily transconductivein the direction of coupling. coupling means primarily transconductivecoupling said arms with opposite polarity in the other direction,whereby said second section has a predeterminedv pass band and apredetermined image impedance across one of said pairs of terminals,said one of said pairs of terminals being coupled to said end of saidfirst filter section, and said coupling means being so proportioned withrespect to the reactive constants of said arms that said image impedanceof said second filter section matches said image impedance of said firstfilter section at their junction.

4. A low-pass filter network comprising a first filter section having apredetermined image impedance at one end and a second active filtersection comprising input and output pairs of terminals, a shuntreactance arm individual to andcoupled to each of said pairs ofterminals and comprising shunt capacitance, said reactance arms havingcoupling means between said arms primarily transconductive in thedirection of'v coupling, means coupling said arms with opposite polarityin the opposite direction, whereby said iii n.so

dit

arenoso 4 sind section h a predetermined pass band and a predetenedimage impedance across one oi said pairs oi terminals. said one oi saidpairs oi terminals being coupled to said end of said t st nlter section,and said coupling means beina so proportioned with respect to thereactive constante oi said arms that said image impedance oi said seconddlter section matches the image impedance ci said ilrst filter sectionat their iunction.

t. n band-pass ter network comprising a first ter section having apredetermined image impedce at one end and an active second lter sectioncomprising input and output pairs oi ternals, a parallel-resonant shunta individual to and coupled to each oi said pairs of terminals,unidirective coupling means between said arms rimarilv transconductivein the direction of coupg, me coupling withopposite polarity said armsin the other ection, whereby said second section has a predeterminedpass band and a predetermined ge impedance across one oi said pairs oiterminals, said one oi said pairs oi terals being coupled to said end ofsaid niet nlter section, and said coupling means being so proportionedwith respect to the reactive constants ci said arms that the imageimpedance ci said second dlter section matches the image impedance oisaid nrst section at their junction.

d. it low-pms ter network comprising a first dlter section having amld-shunt constantc image impedance at one end and an active secondhiter section comprising input and output rs oi terminals, a shuntreactance arm including capacitance individual to and coupled to each cisaid pairs oi terminals, unidirective coupling means in one directionbetween said arms primarilg transconductive in the direction ofcoupling, means coupling said arms with opposite polarity in the otherdirection, whereby said second dlter section has a predetermined passband and constantes mid-shunt image impedance across one oi said paireoi terminals, said one titi oi said paire oi terminals. being coupled tosaid end oi said nist iilter section, and said coupling means being soproportioned with respect to the reactive constants oi said arms thatsaid image impence oi cmd second nlter section matches the imageimpedance oi said nrst dlter section at their inaction, said seconddites section having a phase shiit which varies over a range ci 9i)degrees over the pass band oi seid network.

'i'. it; wave dites network comprising a nrst ter section having amid-shunt constant-lt impedance at one end and an active second nltersection comprising input and output pairs oi' tenais, a reactance t, i ol individual to and coupled to each oi said pairs oiteals, unidirectirecoupling means between said arms primarily trconductive in the directionoi coupling, means coupling said arms with opposite polarity in theother direction. whereby said second nlter section has a predeterminedpass band and a mid-shunt constant-lc image impedance across each oisaid pairs of te als, one ci said pa s oi teinals being coupled to saidend oi said t nlter section, said coupli means being so proportionedwith respect to the reactive constants of said arms that the imageimpedance oi said second utter section matches the im ance oi id nrst@lier-econ attheir junction-and said image imp si ci said second sectionve a constant ratio substantially dit., iereht we unity.

t. A iowss hlter network a t ter between said arms in one directionconsisting primarily oi transconductance gis in the clis rection ofcoupling, unidirective coupling means of opposite polarity between saidarms in the other direction consisting primarily of transconductanceQ21, whereby said second'iilter section has a cutod frequency Y andwhereby said second section has a constant-k mid-shunt image impedanceacross one of said pairs of terminals, said one oi said pairs of terminals being coupled to said end of said first nlter section, and saidcoupling means being so proportioned with respect to the reactiveconstants of said arms that said image impedance of said second ltersection matches the image impedance oi said first illter section attheir junction.

9. in a wave lter network, an active filter section comprising input andoutput pairs ci terminals, a reactance arm individual to and coupled toeach oi said pairs oi' terminals, unidirec-a tive coupling means betweensaid arms in one direction primarily transconductive in the directionof` coupling, coupling means of opposite polaritts between said arms inthe other direction, an mderived termination for said lter sectioncomprising one of said arms, whereby said' lter section has apredetermined cutoil.' frequency and a predetermined constant imageimpedance across one of said pairs of terminals over said band, and aconstant resistance circuit 'connected across said one of said pairs oiterminals.

10. In a wave filter network, an active lter section comprising inputand output pairs ci terminals, a reactance arm individual to and coupledto each oi saidpairs oi terminaladirective coupling means in onedirection between said arms primarily transconductive in the directionci' coupling, and coupling means primarily conductive coupling said armswith opposite polarity in the other direction, an "in-derivedtermination for said lter section comprising one of said arms, wherebysaid Filter section has a predetermined cutoti frequency and apredetermined constant image impedance across one oi said pairs ofterminals over said band, and a constant resistance circuit connectedacross said one of said pairs oi terminals.

11. In a low-pass filter network, an active filter section comprisinginput and output pairs of terminals, a reactance arm individual to andcoupled to each oi said pairs of terminals, dlrective coupling means inone direction between said arms primarily transconductlve in thedirection or coupling, and me coupling said arms with opposite polarityin the vother direction, one oi' said arms consisting oi aseries-connected inductance and condenser, whereby' said section has apredetermined cutod frequency and a sub stantially constant resistiveimage impedance across the pair of terminals to which said one oi saidarms is coupled, anda constant resistance circuit connected across said-ntioned pair oi terminals.

l2. An active lter section comprising input and output rs oi terminals.areactance arm dit dit

of terminals, directive coupling means in :one direction between saidarms primarily transconductive in the direction of coupling, andcoupling means primarily conductive coupling said arms in the otherdirection with opposite polarity, phase-shifting means included in said.con-

'arms with opposite polarity in the other direction,phaseshifting meanscomprising inductance in series with said conductive coupling means andcapacitance in shunt therewith effective to provide regeneration at thecutoff frequency of said section just suiiicient to compensate fordissipation in said section, whereby said section has a predeterminedcutoff frequency and a predetermined image impedance across'one of saidpairs of terminals.

14. A band-pass filter comprising a plurality of coupled filter sectionswith image impedance matching at their junctions, each of two of saidsections comprising a transformer having primary and secondary windings,transoonductive coupling means comprising a vacuum tube having inherentinput and output capacitances coupling thesecondary winding of one ofsaid transformers with the primary winding of the other of saidtransformersvcoupling means of opposite polarity in the other directionbetween said two last-mentioned windings, the coupling eect of saidcoupling means being proportioned with respect to the reactive constantsof said transformers to provide constant-k mid-shunt image impedancesacross said capacitances and a predetermined pass band for said filter,said image impedances matching the image impedances of adjoining ones ofsaid sections.

15. A band-pass filter comprising a plurality of coupled lter sectionswith image impedance matching at their junctions, each of two of saidsections comprising a transformer having primary and secondary windings,transconductive coupling means comprising a vacuum tube having inherentinput and output capacitances coupling the secondary winding of one ofsaid transformers with the primary winding of the other of saidtransformers, coupling means of oppoindividualoto and coupled to each ofsaid pairs- 'site polarity in the other' direction between said twolast-mentioned windings, said couplingI` means comprising a'resistorcoupled between points of said two.l lastmentioned windings, thecoupling eiect of said coupling means being proportioned with respect tothe reactive constants of said transformers to provide constant-1cmid-shunt image impedances across said capacitances 'and a predeterminedpass band for said filter, said image impedances matching the imageimpedances of adjoining ones of said sections.

16. A band-pass lter comprising a plurality of coupled filter sectionswith image impedance matching at their junctions and including twosimilar sections, two shunt reactance arms for each of said sections, atransformer having primary and secondary windings individuallycomprising one of said arms in each of said sections, transconductivecoupling means comprising a vacuum tube inl each of said sectionscoupling its respective arms,- coupling means between said arms in eachof said sections coupling said arms with' opposite polarity in the otherdirection, the coupling eiect of-said coupling means being proportionedwith respect to the reactive constants iov of said similar sections toprovide constant-k mid-shunt image impedances and a predetermined passband for said similar sections, said image impedances matching the imageimpedances of adjoining ones of said sections, said transformer having acoemcient of coupling k=Aw/2w0, where Aw is the width of the pass bandof said similar sections and wo is the mean frequency of said similarsections, Aw being substantially less than so.

17. A wide band iilter network comprising a first filter section havinga predetermined image impedance at one end and an active lter sectioncomprising input and output pairs of terminals, two capacitive shuntarms coupled to said terminals and having unidirective coupling meansbetween said arms primarily transconductive in the direction ofcoupling, said coupling means comprising a vacuum tube having input andoutput capacitances, one of said capacitances of said tube comprisingthe capacitance of a full-shunt element of said iilter network, andmeans coupling said arms with opposite polarity in the other direction,whereby said section has a predetermined pass band and a predeterminedimage impedance across said one of said arms, said one of said pairs ofterminals being coupled to said end of said first iter section, and saidcoupling means being so proportioned with respect to the reactiveconstants ot said arms that the image impedance of said second filtersection matches the image impedance of said first iilter section attheir junction.

HAROLD A. WHEELER.

